The historical observations of stress and strain design inside bone

This is a historical background of tensegrity: the balance of tension to compression in the shape of bone

I came across a book originally published in 1942 by the Cambridge University Press under the title of On Growth and Form: A New Addition by D’Arcy Wentworth Thompson during my sabbatical year as one of the readings I undertook to grasp. I am reading citing from the XVI chapter entitled THE STRENGTH OF MATERIALS. The topic is bone. “Before we speak of the form of a bone, let us say a word about the mechanical properties of the material of which it is built, in relation to the strength it has to manifest or the forces it has to resist: understanding always that we mean thereby the properties of fresh or living bone, with all its organic as well as inorganic constituents, for dead bone is a very different thing. ”

As you can sense from the choice of words, Thompson’s selection comes with a patina of age; we don’t talk generally like this anymore. Our voice and written communication tends to be static, more abrupt almost cryptic in a texting sort of way. Maybe our way of talking is being affected by our twittering type texting, time will tell. But what gets me here I am pontificating about how stiff the choice of his words, but in reality who am I to criticize? Now Thompson gets into the heart of bone strength descriptions. When we wake up bounding to the clatter of an alarm, we jump onto the floor without once thinking how much force gets absorbed as the feet make first contact scrambling at the start of a new workday. We don’t hesitate one second to think of the forces running into our foot bones transmitting up our leg into the pelvic girdle as the daybreak erupts grabbing at the bathroom door for what our cousin calls, la toilette. All these mechanical motions all these transmitted forces running through our entire skeleton, with not a thought about the whole process.

“In all the structures raised by the engineer, in beams, pillars and girders of every kind, provision has to be made, somehow or other, for strength of two kinds, strength to resist compression or crushing, and strength to resist tension or pulling asunder. “ In the case as an example of two columns supporting a beam, “the evenly loaded column is designed to support a downward pressure, the wire-rope, like the tendon of a muscle, is adapted only to resist a tensile stress; but in many or most cases the two functions are very closely inter-related and combined.”

from University of Cambridge DoITPoMS : Structure and composition of bone StressinFemurHead updated   Head of the femur (thigh bone)

The two combined forces are compression and tension, which is what tensegrity is all about. So here we have Thompson’s reflections from 1942 that leap forward to Donald Ingber’s tensegrity essay in Scientific American on The Architecture of Life published in 1998. That is the kind of thing that happens in science. Observations can be totally insightful easily 50 years before they start breaking out of the science jargon world before reaching into the public’s perception.

“ The case of a loaded beam is a familiar one. However, be that as it may, we know, roughly, that when the beam is loaded in the middle and supported at both ends, it tends to be bent into an arc, in which condition its lower fibres are being stretched, or are undergoing a tensile stress, while its upper fibers are undergoing compression. A still more beautiful way of exhibiting the distribution of strain is to use gelatin, into which bubbles of gas have been introduced with the help of sodium bicarbonate. A bar of such gelatin, when bent in a hoop, shows on the side of the bubbles elongated by tension and on the other side those bubbles shortened by compression.”

I love how eloquent the use of a bubble shapes description, it gives such a clean image of the forces that show either compression or strain at the same time. If you’ve ever watched an older man walking along the beach, his legs could be bowed out as a badge of his decades of their use.  “In a like manner a vertical pillar, if unevenly loaded (as for instance the shaft of our thigh-bone normally is), will tend to bend, and so to endure compression on its concave side, and tensile stress upon its convex side. In many cases it is the business of the engineer to separate out, as far as possible the pressure-lines from the tension lines, in order to use separate modes of construction, or even different materials for each. In a suspension-bridge, for instance a great part of the fabric is subject to tensile strain only, and is built throughout of ropes or wires; but the massive piers at either end of the bridge carry the weight of the whole structure and of its load, and endure all the ‘compression-strains’ which are inherent in the system. Very much the same is the case in that wonderful arrangement of struts and ties which constitute, or complete, the skeleton of an animal.

The ‘skeleton’ as we see it in a museum, is a poor and a misleading picture of the (bio) mechanical efficiency. From the engineer’s point of view, it is a diagram showing all the compression-lines, but by no means all of the tension lines of the construction; it shows all the struts, but few of the ties and perhaps we might say none of the principle ones; it falls all to pieces unless we clamp it all together, as best we can in a more or less clumsy and immobilized way. But in life, that fabric of struts is surrounded and interwoven with a complicated system of ties-‘it’s living mantles jointed strong.– With glistening band and silvery thong’: from Oliver Wendell Holmes’ Anatomist’s Hymn, ties are tethering ligament to membrane, with muscle and tendon, running between bone and bone; and the beauty and strength of the mechanical construction lie not in one part or in another, but in the harmonious concatenation which all the parts, soft and hard, rigid and flexible, tension-bearing and pressure bearing, make up together.”

If that isn’t a prescient prediction for a description of tensegrity I am simply stunned at such relevance from 1942. When I contacted Donald Ingber last year asking him via e-mail,’ Is the brain a tensegrity structure?’ since I could find no citations anywhere in the medical literature reflecting the importance of tensegrity shape with the brain. Ingber responded, in a very simple fashion and eloquently told me, basically, how could it not be?

Thompson has brought the balance of compression to tension as it reveals itself in the skeleton. I had my own biases about bone being some sort of static structure that’s just there. Bone is this wondrous dynamic substance that lets us bound out of bed in the morning as we race across our own bedrooms. Bone grows as bones deposit onto bones as bones absorb themselves slightly changing shape all the time, yet all changes unseen, happening beneath our skin. And bones can fracture -that’s when we notice how important they are.

We thought that bones heal at the fracture zone now there is this component of repair coming from within the brain. Orthopedic surgeons have noticed for five decades that head trauma combined with a fracture anecdotally has a faster healing time. “And it is not only in the supporting pillar that such a construction is useful; it is appropriate in every case where stiffness is required, where bending has to be resisted. A sheet of paper becomes a stiff rod when you roll it up, and hollow tubes of thin bent wood withstand powerful thrusts in airplane construction. The long bone of a bird’s wing has little or no weight to carry, but it has to withstand powerful bending moments; and in the arm-bone of a long winged bird, such as the albatross, we see the tubular construction manifested in its perfection, the bony substance being reduced to a thin, perfectly cylindrical, and almost empty shell.”

“Two points, both of considerable importance, present themselves here, and we may deal with them before we go further on. In the first place, in our bending beam the stress is greatest at the middle; if we were to press on our walking stick hard against the ground, it will tend to snap midway. Hence if our cylindrical column be exposed to strong bending stresses, it will be prudent and economical to make its walls thickest in the middle and thinning off gradually towards the ends; and if we look at a longitudinal section of the thigh bone, we shall see that is just what Nature has done. The presence of a ‘danger-point’ has been avoided, and the thickness of the walls becomes nothing less than a diagram, or graph of the bending-moments from one point to another along the length of the bone.”

“The second point requires a little more explanation. If we imagine our loaded beam to be supported at one end only (for instance being built into a wall), so as to form what is called a ‘bracket’ or a ‘cantilever,’ then we can see, without much difficulty, that the lines of stress in the supported beam under the load run like compression lines starting at the wall then veering vertically down ward (looking like the distance perspective of painted track and field lanes) but where the bracket is fastened to the wall there is pressure directed horizontally against the wall in the lower part of the surface of attachment; and the vertical beginning and the horizontal end of these pressure-lines must be continued into one another in the form of some even mathematical curve-which, as it happens, is part of a parabola. The tension lines are identical in form with the compression lines, of which they constitute the ‘mirror-image’; where the two systems intercross they do so at right angles, or ‘orthogonally’ to one another. Yet it is often possible to weaken one set of lines at the expense of the other, and in some cases to do altogether away with one set or the other. For example, when we replace our end-supported beam by a curved bracket, bent upwards or downwards, we have evidently cut away the greater part of the tension lines, and in the other the greater part of the compression lines. It’s as if instead of bridging a stream with our beam of wood we bridge it with a rope, it is evident that this new construction contains all the tension lines but none of the compression lines of the old.” Bones have to grow, that is the dynamic property that tensegrity compression-tension balancing accomplishes and bones age, bending as they change shape supporting the same weight.

“Let us now, at last come to the mechanical structure of bone of which we find a well known and classical illustration in the various bones of the human leg. In the case of the tibia, the bone is somewhat widened out above, and its hollow shaft is capped by an almost flat roof, on which the weight of the body directly rests. It is obvious that, under these circumstances, the engineer would find it necessary to devise means for supporting this flat roof, and for distributing the vertical pressures which impinge upon it to the cylindrical walls of the shaft.”

“But in our bones, and all weight carrying bones in general, the hollow space is filled with marrow, blood vessels and other tissues; and amidst these living tissues lies a fine lattice work of little interlaced ‘trabeculae’ of bone, forming the so called ‘cancellous tissue’. The older anatomists were content to describe this cancellous tissue as a sort of spongy network or irregular honeycomb; but at length its orderly construction began to be perceived, and attempts were made to find a meaning or ‘purpose’ in the arrangement. Sir Charles Bell had a glimpse of the truth when he asserted that ‘this minute lattice work, or the cancelli which constitutes the interior structure of bone, have still references acting on the bone; but he did not succeed in showing what these forces are, nor how the arrangement of the cancelli is related to them.”

VisualHistology Atlas 2-0-71 Cancellous head of the femur bone

‘Bone is marvelous material. There are few substances, natural or man-made, that can match its durable combination of strength and flexibility. The femur of an adult athlete, for example, is so strong it can bear a vertical load of nearly 2000 lbs. Other bones, such as those in the middle ear, are so delicate they can transmit infinitesimally small sound vibrations so accurately that you can hear the exquisite overtones that issue forth from a Guarneri violin.

When tested against well-known man-made materials, bone fares extremely well. It is as strong as cast iron – it has the tensile strength of cast iron and can handle compressive loads as well as cast iron can – and yet is some 20 times more flexible; you can bend a bone 20 times more than a cast iron rod of similar size and shape before it will break. Although some new space-age materials – notably the carbonfiber derivatives such as kevlar and graphite can equal bone’s strength and flexibility per unit of mass, none of these materials can repair itself as bone can.’

Jeffries Wyman from the Boston Society of Natural History in 1849 wrote about animal mechanics: on the cancellated structure of some of the bones of the human body. Wyman came much closer to the truth in a paper seemingly neglected and forgotten. “1. The cancelli of such bones as assist in supporting the weight of the body are arranged either in the direction of that weight, or in such a manner as to support and brace those cancelli which are in that direction. In a mechanical point of view they may be regarded in nearly all these bones as a series of ‘studs’ and ‘braces’. 2. The direction of these fibres in some of the bones of the human skeleton is characteristic and, it is believed, has a definite relation to the erect position which is naturally assumed by man alone.” A few years afterwards the story was told again, and this time with convincing accuracy. “It was shown by Herman Meyer and Julius Wolff that the trabeculae, as seen in the longitudinal section of the femur, spread in beautiful curving lines from the head of the femur to the hollow shaft of the bone; and that these linear bundles are crossed by others, with so nice a regularity of arrangement that each intercrossing is as nearly as possible an orthogonal one: that is to say, the one set of fibres or cancelli cross the other everywhere at right angles. A great engineer, Professor Culmann of Zurich, to whom the method of ‘graphic statics’ was formulated happened to come into his colleague Meyer’s dissecting room in 1866, where the anatomist was contemplating the section of bone.

The engineer, who had been busy designing a new and powerful lifting crane, saw in a moment that the arrangement of the bony trabeculae was nothing more nor less than a diagram of the lines of stress, or directions of tension and compression, in the loaded structure: in short, that Nature was strengthening the bone in precisely the manner and direction in which strength was required’ Professor Culmann is said to have shouted out, ‘That’s my crane!’ ”

It took scientists becoming ambitious to attempt making bone, to grow bone cells into bone structure in the laboratory, they realized bone needed a structure, a scaffold to grow onto and into, with this support mesh, they have begun crude attempts that mimic bone growth. Early attempts from the year 2000 have begun to recognize the contribution of cellular assembly involving bone encompassing stress and strain incorporated into the shape of the design.

Yet the eloquent words of stress and strain echoing from the early pioneers from the late eighteenth century were basically ignored and lost in time.

Their century old voices have now been rekindled to reveal their exquisite observations. It will be up to our own attempted experiments to verify bone metabolism to hopefully open the truth first voiced from the bone tensegrity pioneers whose compelling bone understanding was so far ahead of its time. Bone remodeling is about to catch up to using tensegrity strain-compression shape within bone as the mechanical design to how the brain regulates bone shape. Our question has now a deep heritage behind it, does bone change with minor traumatic brain injury? Does tensegrity based bone changes occur following concussion brain injury? If I were to phrase it another way, bone changes shape as we age bone becomes weaker, the tensegrity balance between bone growth with bone absorption is lost, bone is no longer thicker in areas where Nature designed it to be thicker to better support the forces. As bone diameter changes, bone becomes weaker to fracture more easily. The entire shape design is now longer in harmony of stress with strain. We are attempting to learn the conversation as it were between the bone and the brain, what part of the brain tensegrity link in terms of balance is now off?


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Montreal Grandmother, Agnes Kent was saved by Raul Wallenberg from certain death, when he provided papers for her and her Mom to escape away from the Nazis. Today when asked what that escape meant, she replied,"Remind people, that while statesmen and whole countries remained silent and did nothing, a single individual chose to act, with ramifications that proved enormous. Similar choices confront us today. Write that simple truth she said, it can never be repeated often enough because the world keeps forgetting it."
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